Nearly 600 civil servants and former immigration workers are to be drafted in to help staff Britain's borders during the Olympics, at a cost of more than £2.5m, in an effort to fulfil the government's pledge to check all passports at peak periods during the Games.

Briefing documents for the UK Border Agency staff show plans to employ Home Office and Revenue and Customs civil servants who volunteer for the role, and hundreds of immigration staff who have recently left or retired because of budget cuts.

The volunteers who are to provide "critical incident coverage" at borders are to receive four days' training, including one day of mentoring, and there will be 800 training slots available from the end of June.

They will be stationed at passport control desks at Heathrow, Gatwick, Luton, Bristol and Stansted, but also across northern France at Coquelles, Calais, Dunkirk and Paris.

The 585 extra staff, who will be made available every week to work on the passport desks, will be paid and their travel and accommodation costs reimbursed.

A further 100 short-term staff are to be sent abroad to carry out passport control work at British consulates.

The Home Office's contingency plan comes on top of severe restrictions on UK Border Force and other immigration staff taking leave this summer, especially during the Olympics and Paralympics.

Airport authorities are also drawing up a plan to levy higher landing fees to fund more border staff, in a move that is believed to have the backing of David Cameron.

Willie Walsh, the chief executive of International Airlines Group, which includes British Airways, told BBC Radio 4's Today programme the airlines were prepared to pay the higher landing fees as long as the charges led to a competent service. But he warned: "We are not prepared to pay a government that wastes money."

Walsh said ministerial claims that nobody had waited longer than one and a half hours to get into Britain were untrue, and the continuing passport queue chaos at Heathrow and other airports meant Britain was not open for business. "We need urgent action," he said.

A dedicated fast-track immigration lane is to be set up at Heathrow and other major airports to ensure the 70,000 members of the "Olympic family", including competitors, officials and overseas media, can bypass passport queues.

Immigration worker unions have criticised the plan, including the restrictions on leave, as excessive and unnecessary. The immigration minister, Damian Green, made a hurriedly arranged visit to Heathrow to announce the establishment of "flying squad" mobile teams to respond to peaks in arrivals at the airport, and plans to make 80 extra staff available on the busiest days.

"We recognise the need to minimise disruption while we secure the border, which is why from today our preparations for managing summer traffic at airports come into effect," Green said.

Cameron was reported to have told ministers to admit there was a problem at Heathrow after a update meeting with the home secretary Theresa May on Tuesday morning. "We've got to grip this," he is reported to have said.

Unions described the promise of immediate extra staff being drafted in from other parts of UKBA as "putting a sticking plaster on a serious injury".

BAA already levies more than £1bn in annual landing charges at Heathrow, with some of the money paying for new technology, including the automatic e-passport gates. A major issue in the argument over delays at passport checks is the government's decision to cut UK Border Force staff by 18% over the next three years, a reduction critics say is beginning to bite.

The shadow home secretary, Yvette Cooper, published leaked management figures showing that about 880 posts had been cut from the UK Border Force since 2010, reducing numbers to 7,988 in March 2012, and a further 1,550 could go by 2014-15 as a result of budget cuts.